cp's OEIS Frontend

A333863 Number of Hamiltonian paths in a 2*(2*n+1) X (2*n+1) grid starting at the upper left corner and finishing in the lower right corner.

%I A333863 #27 Jun 29 2023 11:01:14
%S A333863 1,16,117204,440051896440,825830699757513748579,
%T A333863 769203260676279544212492116449800,
%U A333863 354179806054404909542325896762875458037457353029,80433401895946253522491939742836167238530417144721958187080077425
%N A333863 Number of Hamiltonian paths in a 2*(2*n+1) X (2*n+1) grid starting at the upper left corner and finishing in the lower right corner.
%H A333863 Ed Wynn, <a href="/A333863/b333863.txt">Table of n, a(n) for n = 0..9</a>
%F A333863 a(n) = A333580(2*(2*n+1), 2*n+1).
%o A333863 (Python)
%o A333863 # Using graphillion
%o A333863 from graphillion import GraphSet
%o A333863 import graphillion.tutorial as tl
%o A333863 def A333863(n):
%o A333863     universe = tl.grid(4 * n + 1, 2 * n)
%o A333863     GraphSet.set_universe(universe)
%o A333863     start, goal = 1, 2 * (2 * n + 1) ** 2
%o A333863     paths = GraphSet.paths(start, goal, is_hamilton=True)
%o A333863     return paths.len()
%o A333863 print([A333863(n) for n in range(7)])
%Y A333863 Cf. A001184, A333580, A333585, A333864.
%K A333863 nonn
%O A333863 0,2
%A A333863 _Seiichi Manyama_, Apr 08 2020
%E A333863 More terms from _Ed Wynn_, Jun 28 2023